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2823
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(
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[
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16
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c
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[
17
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,
p
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Evaluation Warning : The document was created with Spire.PDF for Python.
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r
i
t
h
m
(
F
F
OA
)
[
19
]
.
O
u
r
c
o
n
t
r
i
b
u
t
i
o
n
s
i
n
t
h
i
s
p
a
p
e
r
a
r
e
d
e
s
c
r
i
b
e
d
as
f
o
l
l
o
ws
:
−
Pro
p
o
s
ed
clu
s
ter
h
ea
d
s
elec
tio
n
u
s
in
g
g
r
ey
wo
lf
o
p
tim
izatio
n
with
en
er
g
y
ef
f
icien
t
p
ar
am
e
ter
s
.
−
P
r
o
p
o
s
e
d
a
n
o
b
j
e
c
t
i
v
e
f
u
n
c
t
i
o
n
a
n
d
w
e
i
g
h
t
p
a
r
a
m
e
t
e
r
s
t
o
s
e
l
e
c
t
t
h
e
o
p
t
i
m
a
l
C
H
s
a
n
d
e
f
f
i
c
i
e
n
t
c
l
u
s
t
e
r
f
o
r
m
a
t
i
o
n
.
−
T
ested
p
r
o
p
o
s
ed
wo
r
k
with
v
a
r
io
u
s
W
SN scen
ar
io
s
an
d
ef
f
ic
ac
y
co
m
p
a
r
ed
with
o
t
h
er
alg
o
r
ith
m
s
.
T
h
e
r
est
o
f
t
h
e
p
a
p
er
f
o
r
m
u
lat
ed
as
f
o
llo
ws.
Sectio
n
2
d
ea
ls
with
th
e
liter
atu
r
e
s
tu
d
y
o
f
th
e
ex
is
tin
g
m
ec
h
an
is
m
t
o
s
elec
t
th
e
clu
s
t
er
h
ea
d
s
.
Sectio
n
3
d
is
cu
s
s
ed
th
e
p
r
elim
in
ar
ies
o
f
GW
O
alg
o
r
ith
m
an
d
en
e
r
g
y
co
n
s
u
m
p
tio
n
m
o
d
els.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
o
lo
g
ies
w
ith
its
f
o
r
m
u
lated
o
b
jectiv
e
f
u
n
ctio
n
an
d
weig
h
t
p
ar
am
eter
f
o
r
clu
s
ter
f
o
r
m
atio
n
p
r
esen
ted
in
s
ec
tio
n
4
.
T
h
e
e
x
p
er
im
e
n
tatio
n
r
esu
lts
ar
e
d
is
cu
s
s
ed
in
s
ec
tio
n
5
an
d
f
in
ally
,
co
n
clu
s
io
n
an
d
f
u
tu
r
e
wo
r
k
s
a
r
e
p
r
o
v
id
ed
i
n
s
ec
tio
n
6.
2.
L
I
T
T
E
RA
T
UR
E
RE
V
I
E
W
V
a
s
t
r
e
s
e
a
r
c
h
h
a
s
b
e
e
n
p
l
u
n
g
e
d
i
n
t
h
e
a
r
e
a
o
f
w
i
r
e
l
e
s
s
s
e
n
s
o
r
n
e
t
w
o
r
k
s
i
n
o
r
d
e
r
t
o
p
e
r
p
e
t
u
a
t
e
t
h
e
l
i
f
e
t
i
m
e
o
f
t
h
e
n
e
t
w
o
r
k
.
S
i
n
c
e
t
h
e
s
e
l
e
c
t
i
o
n
o
f
c
l
u
s
t
e
r
h
e
a
d
s
i
s
a
n
N
P
-
h
a
r
d
p
r
o
b
l
e
m
e
a
c
h
a
l
g
o
r
i
t
h
m
h
a
s
i
t
s
o
w
n
f
l
a
w
s
a
s
w
e
l
l
.
A
l
g
o
r
i
t
h
m
s
d
e
v
i
s
e
d
f
o
r
i
n
c
r
e
a
s
i
n
g
t
h
e
l
o
n
g
e
v
i
t
y
o
f
t
h
e
n
e
t
w
o
r
k
c
a
n
b
e
b
r
o
a
d
l
y
c
a
t
e
g
o
r
i
z
e
d
i
n
t
o
1
)
h
e
u
r
i
s
t
i
c
a
n
d
2
)
m
e
t
a
-
h
e
u
r
i
s
t
i
c
a
p
p
r
o
a
c
h
e
s
.
E
l
a
b
o
r
a
t
i
o
n
s
o
f
t
h
e
s
e
a
p
p
r
o
a
c
h
e
s
a
r
e
a
s
f
o
l
l
o
w
s
:
2
.
1
.
H
euristic
-
ba
s
ed
clu
s
t
er
i
ng
a
lg
o
rit
hm
Sin
ce
d
iv
er
s
e
alg
o
r
ith
m
s
ca
t
er
in
g
to
d
if
f
e
r
en
t
n
ee
d
s
ar
e
th
er
e,
l
o
w
-
en
er
g
y
a
d
ap
tiv
e
clu
s
ter
in
g
(
L
E
AC
H
)
[
20
]
is
o
f
th
e
p
r
ed
o
m
in
an
t
clu
s
ter
in
g
alg
o
r
ith
m
wh
ich
elec
ts
th
e
clu
s
t
er
h
ea
d
wi
th
s
o
m
e
f
ea
s
ib
ilit
y
.
I
t
p
r
o
v
i
d
es
ag
g
r
e
g
atio
n
o
f
th
e
cr
am
m
ed
d
ata
t
h
u
s
r
ed
u
cin
g
th
e
u
n
wan
ted
tr
a
f
f
ic
an
d
en
er
g
y
co
n
s
u
m
p
tio
n
o
f
th
e
n
etwo
r
k
[
21
]
,
th
er
eb
y
in
cr
ea
s
in
g
th
e
lo
n
g
e
v
i
ty
o
f
t
h
e
n
et
wo
r
k
.
Ho
wev
e
r
,
it
d
o
es
n
o
t
p
r
o
v
id
e
an
y
ad
eq
u
ate
in
f
o
r
m
atio
n
ab
o
u
t
th
e
n
u
m
b
er
o
f
clu
s
ter
h
ea
d
s
in
a
n
etwo
r
k
.
So
m
etim
es
it
m
ay
o
p
t
a
n
o
d
e
with
lo
w
en
er
g
y
as
a
clu
s
ter
h
ea
d
th
er
e
b
y
s
h
o
r
t
en
in
g
th
e
life
tim
e
o
f
th
e
n
e
two
r
k
.
Oth
er
m
o
s
t
p
o
p
u
lar
alg
o
r
i
th
m
s
in
clu
d
e
p
o
wer
-
ef
f
icie
n
t
g
ath
er
in
g
in
s
en
s
o
r
in
f
o
r
m
atio
n
s
y
s
tem
s
(
PEGA
SIS
)
an
d
h
y
b
r
id
en
e
r
g
y
-
ef
f
icien
t
d
is
tr
ib
u
ted
(
HE
E
D
)
.
PEGA
SIS
[
22
]
is
an
ad
d
en
d
u
m
t
o
th
at
o
f
L
E
AC
H
p
r
o
to
co
l.
I
t
is
m
o
r
e
ad
v
an
t
ag
eo
u
s
in
th
e
s
en
s
e
b
ec
au
s
e
it
ag
g
r
eg
ates
all
th
e
d
a
ta
an
d
s
en
d
s
it
to
th
e
ce
n
tr
al
p
r
o
ce
s
s
in
g
u
n
it.
Ho
wev
er
,
it
in
t
r
o
d
u
ce
s
an
a
d
d
itio
n
a
l
lag
if
n
o
d
es
ar
e
d
is
tan
t.
I
t
is
u
n
s
u
itab
le
f
o
r
lar
g
e
s
ca
le
W
SNs
wh
ich
in
v
o
lv
es
m
u
lti
-
h
o
p
co
m
m
u
n
icatio
n
.
HE
E
D
[
23
]
is
also
an
ex
ten
s
io
n
o
f
th
e
L
E
AC
H;
it
s
u
f
f
er
s
f
r
o
m
s
er
io
u
s
co
m
m
u
n
icatio
n
o
v
e
r
h
ea
d
b
etwe
en
a
clu
s
ter
h
ea
d
an
d
a
b
ase
s
tat
io
n
.
I
n
t
h
e
ca
s
e
o
f
E
-
L
E
AC
H
[
1
4
]
,
t
h
e
clu
s
ter
h
ea
d
co
m
m
u
n
icati
o
n
b
etwe
en
d
if
f
er
e
n
t
clu
s
ter
s
is
h
ig
h
ly
ef
f
icien
t,
b
u
t
in
th
e
ca
s
e
o
f
lar
g
er
n
etwo
r
k
s
,
it
f
ails
to
s
elec
t
th
e
n
o
d
es
with
lo
w
en
er
g
y
.
TL
-
L
E
AC
H
[
24
]
in
cr
ea
s
es
th
e
life
tim
e
o
f
th
e
n
etwo
r
k
,
b
u
t
it
w
astes
th
e
e
n
e
r
g
y
w
h
ile
p
er
f
o
r
m
i
n
g
co
m
m
u
n
icatio
n
b
etwe
en
clu
s
ter
h
ea
d
s
an
d
th
e
o
th
er
n
o
d
es.
M
-
L
E
AC
H
ca
r
r
ies
an
ad
v
an
tag
e
b
y
co
n
s
id
er
in
g
m
o
b
ilit
y
in
a
r
o
u
tin
g
p
r
o
to
c
o
l.
I
t
ass
u
m
es
th
at
all
th
e
n
o
d
es
ar
e
co
n
g
r
u
en
t,
a
n
d
it
d
o
es
n
o
t
ca
r
e
a
b
o
u
t
th
e
f
o
r
m
atio
n
o
f
th
e
clu
s
ter
w
h
ile
clu
s
ter
in
g
.
B
-
L
E
AC
H
[
2
5
]
is
an
o
th
er
ex
ten
s
io
n
wh
er
e
th
e
co
m
m
u
n
icatio
n
is
en
tire
ly
d
ep
en
d
in
g
u
p
o
n
th
e
p
o
s
itio
n
o
f
t
h
e
clu
s
ter
h
ea
d
s
wh
ich
n
ee
d
s
n
o
in
f
o
r
m
atio
n
ab
o
u
t
all
th
e
o
th
e
r
n
o
d
es
in
s
id
e
th
e
clu
s
ter
.
T
h
er
ef
o
r
e,
t
h
e
r
esid
u
al
en
er
g
y
o
f
th
e
C
Hs g
et
s
d
r
a
in
ed
wh
ich
f
u
r
th
er
r
ed
u
ce
s
th
e
life
tim
e
o
f
th
e
n
etwo
r
k
.
L
E
AC
H
-
C
[
2
6
,
2
7
]
o
u
tp
er
f
o
r
m
s
L
E
AC
H
-
A,
L
E
AC
H
-
B
,
an
d
MT
E
b
ec
a
u
s
e
th
e
ce
n
tr
al
p
r
o
ce
s
s
in
g
u
n
it
tak
es
ca
r
e
o
f
th
e
lo
ca
tio
n
a
n
d
th
e
e
n
er
g
y
o
f
all
th
e
n
o
d
es
in
th
e
n
etwo
r
k
,
h
e
n
ce
clu
s
ter
f
o
r
m
atio
n
an
d
c
lu
s
te
r
m
ain
ten
an
ce
will
n
o
t
g
et
af
f
ec
ted
.
T
h
e
o
n
ly
d
is
ad
v
an
tag
e
is
th
at
it
is
n
o
t
v
ig
o
r
o
u
s
.
E
-
L
E
A
C
H
is
m
u
ch
en
er
g
y
ef
f
icien
t
in
ca
s
e
o
f
m
u
lti
-
h
o
p
c
o
m
m
u
n
icatio
n
.
I
t
e
n
h
an
ce
s
th
e
clu
s
ter
h
ea
d
s
elec
tio
n
p
r
o
ce
s
s
b
y
co
n
s
id
er
in
g
t
h
e
h
ig
h
er
r
esid
u
al
e
n
er
g
y
a
v
aila
b
l
e
a
t
a
p
ar
ticu
lar
tim
e
with
in
a
c
lu
s
ter
.
T
h
o
u
g
h
V
-
L
E
AC
H
[
28
]
h
as
b
ee
n
p
r
o
p
o
s
ed
as a
n
alter
n
ativ
e
to
L
E
AC
H,
it e
lects a
d
d
itio
n
al
C
Hs to
th
at
o
f
m
ain
C
Hs in
o
r
d
e
r
to
m
itig
ate
th
e
f
ailu
r
e
o
f
th
e
m
ain
C
Hs.
Hen
ce
wh
en
ev
er
th
e
m
ain
C
Hs,
f
ails
th
e
ad
d
itio
n
al
C
H
s
s
el
ec
ted
tak
es
ca
r
e
o
f
its
p
o
s
itio
n
an
d
p
er
f
o
r
m
th
e
f
l
o
o
d
in
g
.
T
h
e
alg
o
r
ith
m
s
u
f
f
er
s
f
r
o
m
d
e
p
r
iv
atio
n
th
at
it
d
o
es
n
o
t
b
o
th
er
a
b
o
u
t
t
h
e
clu
s
ter
f
o
r
m
atio
n
p
r
o
ce
s
s
.
2
.
2
.
M
et
a
-
heuris
t
ic
a
pp
ro
a
c
hes
Me
ta
-
Heu
r
is
tic
alg
o
r
ith
m
s
ac
t
as
th
e
m
o
s
t
p
r
o
m
is
in
g
ap
p
r
o
a
c
h
f
o
r
NP
-
h
ar
d
co
m
b
i
n
ato
r
ial
p
r
o
b
lem
s
.
Sin
ce
th
ey
m
im
ic
f
r
o
m
n
atu
r
e,
it
co
n
ce
n
tr
ates
m
ain
ly
o
n
th
e
asp
ir
an
t
wh
ich
h
as
a
h
ig
h
s
u
r
v
iv
al
r
ate.
Me
ta
-
h
eu
r
is
tic
alg
o
r
ith
m
s
ar
e
b
r
o
ad
ly
ca
teg
o
r
ized
in
to
tw
o
t
y
p
es n
am
ely
ev
o
lu
tio
n
a
r
y
an
d
s
war
m
in
tellig
en
ce
ap
p
r
o
ac
h
es
[
29
]
.
Gen
etic
alg
o
r
ith
m
[
1
5
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3
1
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3
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h
e
a
d
s
e
l
e
c
t
i
o
n
a
l
g
o
r
i
t
h
m
s
.
3.
M
E
T
H
O
DS
3
.
1
.
G
re
y
wo
lf
o
ptim
iza
t
i
o
n
G
r
e
y
wo
lf
o
p
tim
izatio
n
[
2
8
]
is
a
r
ec
e
n
tly
p
r
o
p
o
s
ed
s
war
m
in
tellig
en
ce
al
g
o
r
ith
m
wh
i
ch
m
im
ics
th
e
in
tellig
en
t b
e
h
av
io
r
o
f
g
r
e
y
wo
lv
es wh
ich
in
clu
d
es lea
d
e
r
s
h
ip
an
d
h
u
n
tin
g
ch
ar
ac
ter
is
tics
o
f
th
e
g
r
e
y
wo
lf
.
Gr
ey
wo
lf
wo
r
k
s
in
a
p
ac
k
o
f
5
-
1
2
m
em
b
er
s
wh
ich
f
o
llo
w
s
a
v
er
y
s
tr
ict
s
o
cial
h
ier
ar
ch
y
.
Gr
ey
wo
lf
p
ac
k
co
n
s
is
ts
o
f
f
o
u
r
le
v
el
h
ier
a
r
ch
y
n
am
el
y
alp
h
a,
b
eta,
d
elta,
a
n
d
o
m
eg
a.
Alp
h
a
is
th
e
f
ir
s
t
lev
el
in
t
h
e
h
ier
ar
ch
y
wh
ich
is
co
n
s
id
er
ed
as
th
e
f
ir
s
t
lead
er
o
f
th
e
p
ac
k
.
I
t
is
r
esp
o
n
s
ib
le
f
o
r
all
th
e
d
ec
is
io
n
m
a
k
in
g
a
p
r
o
ce
s
s
lik
e
h
u
n
tin
g
th
e
p
r
ey
,
ap
p
r
o
a
ch
in
g
th
e
p
r
ey
an
d
in
s
tr
u
ctin
g
t
h
e
wo
lv
es
in
th
e
en
tire
p
ac
k
.
T
h
e
s
ec
o
n
d
lev
el
in
th
e
h
ier
ar
ch
y
is
b
eta
,
wh
ich
g
u
id
es
th
e
alp
h
a
in
d
ec
is
io
n
m
a
k
in
g
an
d
also
ac
ts
as
alp
h
a
wh
en
ev
er
th
e
alp
h
a
is
p
ass
ed
awa
y
.
I
n
m
o
s
t
ca
s
es,
b
eta
is
also
ca
lled
as
s
u
b
o
r
d
in
at
e
wo
lv
es.
Delta
is
th
e
th
ir
d
le
v
el
in
th
e
h
ie
r
ar
ch
y
wh
ich
also
k
n
o
w
n
as
ca
r
etak
e
r
an
d
f
i
n
ally
.
Om
eg
a
is
th
e
last
lev
el
in
th
e
h
ier
a
r
ch
y
w
h
ich
o
b
ey
s
th
e
d
ec
is
io
n
o
f
th
e
th
r
ee
ab
o
v
e
lead
e
r
s
an
d
also
m
ain
tain
s
th
e
s
af
ety
an
d
i
n
teg
r
ity
in
th
e
wo
lf
p
ac
k
.
GW
O
wo
r
k
in
g
p
r
o
ce
s
s
is
m
ath
em
atica
lly
m
o
d
elled
as
f
o
llo
ws:
3
.
1
.
1
.
E
ncircling
pro
ce
s
s
All
th
e
g
r
ey
wo
lv
es
in
th
e
p
ac
k
s
tar
t
en
cir
clin
g
th
e
p
r
e
y
b
ef
o
r
e
it
s
tar
ts
th
e
h
u
n
tin
g
p
r
o
ce
s
s
.
T
h
e
en
cir
clin
g
p
r
o
ce
s
s
is
m
ath
em
atic
ally
f
o
r
m
u
lated
an
d
it is
g
iv
en
i
n
th
e
(
1
)
a
n
d
(
2
)
.
⃗
⃗
=
|
.
⃗
⃗
⃗
⃗
(
)
−
(
)
|
(
1
)
(
+
1
)
=
|
⃗
⃗
⃗
⃗
(
)
−
.
⃗
⃗
|
(
2
)
w
h
e
r
e
,
⃗
⃗
r
e
p
r
e
s
e
n
t
s
t
h
e
d
i
s
t
a
n
c
e
b
e
t
w
e
e
n
t
h
e
p
r
e
y
a
n
d
w
o
l
f
,
d
e
t
e
r
m
i
n
e
s
t
h
e
c
u
r
r
e
n
t
p
o
s
i
t
i
o
n
o
f
t
h
e
w
o
l
f
i
n
i
t
e
r
a
t
i
o
n
s
a
n
d
⃗
⃗
⃗
⃗
i
s
t
h
e
p
o
s
i
t
i
o
n
o
f
t
h
e
p
r
e
y
.
T
h
e
c
o
n
s
t
a
n
t
p
a
r
a
m
e
t
e
r
s
a
n
d
a
r
e
m
e
a
s
u
r
e
d
u
s
i
n
g
t
h
e
(
3
)
a
n
d
(
4
)
.
=
2
.
1
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
−
(
3
)
=
2
.
2
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
2
8
2
2
-
2
8
3
3
2826
wh
er
e
,
1
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
an
d
1
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
d
eter
m
in
es
t
h
e
ar
b
itra
r
y
v
ec
to
r
s
g
en
er
ated
b
etw
ee
n
th
e
r
an
g
e
o
f
[
0
,
1
]
.
T
h
ese
v
alu
es
aid
s
to
ad
ju
s
t
th
e
p
o
s
itio
n
o
f
t
h
e
g
r
ey
wo
lf
r
an
d
o
m
ly
at
an
y
p
o
s
itio
n
to
war
d
s
th
e
p
r
ey
.
Par
am
eter
is
aid
s
to
co
n
tr
o
l th
e
m
o
v
em
e
n
t o
f
th
e
a
lg
o
r
ith
m
wh
ich
lin
ea
r
ly
r
e
d
u
c
es f
r
o
m
2
t
o
0
o
v
er
ce
r
tain
g
en
er
atio
n
s
.
3
.
1
.
2
.
H
un
t
ing
pro
ce
s
s
I
n
th
e
h
u
n
tin
g
p
r
o
ce
s
s
,
all
th
e
d
o
m
in
an
t
wo
lv
es
ad
ju
s
t
th
eir
p
o
s
itio
n
s
u
s
in
g
n
o
n
-
d
o
m
i
n
an
t
wo
lv
es
,
,
an
d
.
T
h
e
p
o
s
itio
n
u
p
d
ate
u
s
in
g
th
ese
n
o
n
-
d
o
m
in
an
t
wo
lv
es
h
av
e
m
ath
em
atica
lly
m
o
d
elled
an
d
it
is
g
iv
en
in
(5
-
7
)
.
⃗
⃗
⃗
⃗
⃗
=
|
1
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
2
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
−
|
,
⃗
⃗
⃗
⃗
=
|
3
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
−
|
(
5
)
1
⃗
⃗
⃗
⃗
=
|
⃗
⃗
⃗
⃗
−
1
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
⃗
|
,
2
⃗
⃗
⃗
⃗
=
|
⃗
⃗
⃗
⃗
−
2
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
|
,
3
⃗
⃗
⃗
⃗
=
|
⃗
⃗
⃗
⃗
−
3
⃗
⃗
⃗
⃗
.
⃗
⃗
⃗
⃗
|
(
6
)
Usi
n
g
in
(
5
)
a
n
d
(
6
)
ar
e
u
s
ed
t
o
u
p
d
ate
th
e
p
o
s
itio
n
o
f
th
e
g
r
ey
wo
lf
an
d
it is
s
h
o
wn
in
(
7
)
.
(
+
1
)
=
0
.
33
∗
∑
⃗
⃗
⃗
3
=
1
(
7
)
T
h
e
p
o
s
itio
n
u
p
d
ate
u
s
in
g
alp
h
a,
b
eta
an
d
d
elta
ar
e
g
r
ap
h
ica
lly
r
ep
r
esen
ted
in
Fig
u
r
e
2.
Fig
u
r
e
2
.
Po
s
i
tio
n
u
p
d
ate
in
GW
O
3.
1
.
3
.
Seek
ing
a
nd
a
t
t
a
c
k
ing
t
he
prey
T
h
e
p
ar
am
eter
is
a
r
an
d
o
m
v
ec
to
r
wh
ich
is
u
s
ed
to
e
x
p
l
o
r
e
an
d
e
x
p
lo
it
th
e
s
ea
r
c
h
p
o
s
itio
n
o
f
th
e
g
r
ey
wo
lv
es.
E
v
e
r
y
co
u
r
s
e
o
f
iter
atio
n
s
,
th
is
p
a
r
am
eter
h
as
b
ee
n
a
d
ju
s
ted
in
th
e
r
an
g
e
o
f
[
−
,
]
,
wh
er
e
th
e
v
alu
e
lin
e
ar
ly
d
ec
r
ea
s
es
f
r
o
m
2
to
0
.
GW
O
alg
o
r
ith
m
e
x
p
lo
its
th
e
p
r
ey
if
|
|
<
1
o
th
er
wis
e
i
t
s
ee
k
s
f
o
r
n
ew
p
r
ey
i
f
|
|
>
1
.
I
n
ad
d
itio
n
to
th
at
,
p
ar
am
eter
lies
in
th
e
r
an
g
e
o
f
[
0
,
2
]
wh
ich
ai
d
s
th
e
alg
o
r
ith
m
to
av
o
i
d
th
e
lo
ca
l
o
p
tim
a
s
tag
n
atio
n
b
y
p
r
o
v
id
i
n
g
s
o
m
e
r
an
d
o
m
weig
h
t
to
th
e
p
o
s
itio
n
u
p
d
at
e.
Ho
wev
er
,
t
u
n
in
g
th
e
p
ar
am
ete
r
p
r
o
v
id
es
b
ette
r
r
esu
lts
co
m
p
a
r
e
to
th
e
g
en
e
r
ic
GW
O
alg
o
r
ith
m
.
I
n
th
is
p
r
o
p
o
s
ed
wo
r
k
,
we
tu
n
ed
th
e
p
ar
am
eter
f
o
r
b
etter
r
esu
lts
.
T
h
e
wo
r
k
in
g
f
lo
w
o
f
t
h
e
GW
O
al
g
o
r
ith
m
is
m
ath
em
atica
lly
m
o
d
elled
an
d
it is
s
h
o
wn
in
alg
o
r
ith
m
1
.
Alg
o
r
ith
m
1
:
Gr
e
y
wo
lf
o
p
tim
izatio
n
alg
o
r
ith
m
Input
–
Initialize the population size of the wolves
=
(
1
,
2
,
3
,
…
)
and parameters A, C
Step 1:
Randomly generate
solutions
with
in the boundary regions
Step 2:
Evaluate the fitness of the wolves
St
ep
3:
Se
le
ct
th
e
fi
rs
t
be
st
so
lu
ti
on
as
Al
ph
a
,
se
co
nd
be
st
as
beta
,
th
ir
d
be
st
as
De
lt
a
and rest as Omega.
Step 4:
Update the position of the grey wolves an
d its parameters
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
n
en
erg
y
-
efficien
t c
lu
s
ter h
e
a
d
s
elec
tio
n
in
w
ir
eless
s
en
s
o
r
n
etw
o
r
k
u
s
in
g
… (
K
a
u
s
h
ik
S
ek
a
r
a
n
)
2827
Step 5
:
Evaluate the new fitness of all wolves
Step 6:
Update the alpha, beta, and delta
Step 7:
Repeat step 5 to 7 until condition satisfies
Output
–
visualize the Alpha wolf
3
.
2
.
E
nerg
y
c
o
ns
um
ptio
n m
o
del
I
n
th
is
p
a
p
er
,
th
e
en
e
r
g
y
co
n
s
u
m
p
tio
n
m
o
d
el
is
u
s
ed
b
a
s
ed
o
n
th
e
s
u
g
g
esti
o
n
s
o
f
th
e
au
th
o
r
in
[
36
]
.
I
n
th
is
m
o
d
el,
th
e
en
er
g
y
h
as
b
ee
n
u
tili
ze
d
b
y
th
e
tr
an
s
m
itter
an
d
r
ec
eiv
er
f
o
r
tr
an
s
m
itti
n
g
an
d
r
ec
eiv
in
g
th
eir
s
ig
n
als an
d
to
o
p
e
r
ate
th
e
r
ad
i
o
am
p
lifie
r
s
.
T
h
e
en
er
g
y
c
o
n
s
u
m
p
tio
n
o
f
a
s
en
s
o
r
f
o
r
tr
a
n
s
m
itti
n
g
(
)
n
-
b
it o
f
in
f
o
r
m
atio
n
is
m
ath
em
atica
lly
r
ep
r
esen
ted
in
(
8
)
.
(
,
)
=
{
×
+
×
×
2
×
+
×
×
4
<
≥
(
8
)
wh
er
e,
r
ep
r
ese
n
ted
as
en
e
r
g
y
u
tili
ze
d
p
er
b
it
to
o
p
er
ate
t
h
e
tr
a
n
s
m
itter
o
r
r
ec
eiv
er
.
an
d
d
eter
m
in
e
d
as
th
e
f
r
ee
s
p
ac
e
m
o
d
el
an
d
m
u
ltip
ath
o
f
am
p
lific
atio
n
p
o
we
r
.
an
d
d
en
o
ted
as
th
e
th
r
esh
o
ld
an
d
d
is
tan
ce
f
o
r
tr
an
s
m
itti
n
g
t
h
e
in
f
o
r
m
atio
n
f
r
o
m
o
n
e
s
en
s
o
r
lo
ca
tio
n
t
o
o
t
h
er
s
en
s
o
r
s
.
At
th
e
s
am
e
tim
e,
en
er
g
y
c
o
n
s
u
m
ed
b
y
th
e
r
ec
ei
v
er
f
o
r
r
e
c
eiv
in
g
n
-
b
it
o
f
in
f
o
r
m
atio
n
(
(
)
)
is
co
m
p
u
ted
as
f
o
llo
ws
;
(
)
=
×
(
9
)
T
h
e
to
tal
en
er
g
y
c
o
n
s
u
m
p
tio
n
(
)
o
f
a
s
en
s
o
r
n
o
d
e
f
o
r
tr
an
s
m
itti
n
g
an
d
r
ec
eiv
in
g
th
e
-
b
it
in
f
o
r
m
atio
n
is
m
ath
em
atica
lly
ca
lcu
lated
as f
o
llo
ws
;
=
(
,
)
+
(
)
(
1
0
)
A
s
en
s
o
r
n
o
d
e
life
tim
e
is
co
m
p
u
ted
b
ased
o
n
th
e
in
itial
en
er
g
y
o
f
th
e
n
o
d
e
an
d
th
e
r
e
m
a
in
in
g
en
er
g
y
o
f
t
h
e
nod
e
af
te
r
tr
an
s
m
itti
n
g
an
d
r
ec
eiv
in
g
th
e
-
b
it in
f
o
r
m
atio
n
.
I
t i
s
ex
p
r
ess
ed
as f
o
llo
ws
;
=
(
1
1
)
wh
er
e,
r
ep
r
esen
ts
in
itial
e
n
e
r
g
y
o
f
t
h
e
s
en
s
o
r
n
o
d
e
(
i.e
.
2
J
in
o
u
r
w
o
r
k
)
an
d
r
ep
r
ese
n
ted
as
th
e
to
tal
co
n
s
u
m
ed
th
e
en
er
g
y
o
f
th
e
s
en
s
o
r
n
o
d
e.
I
n
o
u
r
wo
r
k
,
th
e
n
etwo
r
k
life
tim
e
c
o
n
s
id
er
ed
b
ased
o
n
th
e
n
u
m
b
er
o
f
iter
atio
n
s
u
n
til t
h
e
last
n
o
d
e
o
f
d
ea
th
.
4.
P
RO
P
O
SE
D
AL
G
O
R
I
T
H
M
T
h
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
m
ai
n
l
y
co
n
tr
ib
u
tes
to
s
elec
tin
g
th
e
c
lu
s
ter
h
ea
d
s
b
y
co
n
s
id
er
in
g
th
e
r
esid
u
al
en
er
g
y
an
d
d
is
tan
ce
m
ea
s
u
r
e
m
en
t
o
f
th
e
s
en
s
o
r
n
o
d
es.
I
n
it
ially
,
all
th
e
s
en
s
o
r
n
o
d
es
s
en
d
th
eir
in
f
o
r
m
atio
n
(
n
o
d
e
_
id
,
r
esid
u
al
en
er
g
y
,
lo
c
atio
n
)
to
t
h
e
b
ase
s
tatio
n
.
O
u
r
p
r
o
p
o
s
ed
GW
O
alg
o
r
ith
m
ex
ec
u
ted
at
th
e
b
ase
s
tatio
n
to
s
elec
t
th
e
o
p
tim
al
C
H
(
i.e
.
b
y
s
en
s
o
r
n
o
d
e
in
f
o
r
m
a
tio
n
)
an
d
to
f
o
r
m
th
e
o
p
tim
al
clu
s
ter
s
.
I
n
o
r
d
e
r
to
p
r
o
ce
s
s
th
e
clu
s
ter
f
o
r
m
atio
n
,
we
h
av
e
f
o
r
m
u
lated
th
e
weig
h
t
f
u
n
ctio
n
wh
ich
i
n
v
o
lv
es
th
e
in
tr
a
-
clu
s
ter
d
is
tan
ce
in
f
o
r
m
ati
o
n
,
r
esid
u
al
e
n
er
g
y
,
an
d
n
eig
h
b
o
r
h
o
o
d
r
atio
o
f
C
Hs r
esp
ec
tiv
ely
.
4
.
1
.
T
he
o
bje
ct
iv
e
f
un
ct
io
n f
o
r
CH
s
elec
t
io
n
I
n
th
is
w
o
r
k
,
we
d
er
iv
ed
th
e
o
b
jectiv
e
f
u
n
ctio
n
wh
ich
u
t
ilizes
th
e
in
tr
a
-
clu
s
ter
d
is
tan
ce
am
o
n
g
th
e
s
en
s
o
r
s
an
d
th
e
d
is
tan
ce
f
r
o
m
th
e
tar
g
et
n
o
d
e
.
L
et
u
s
ass
u
m
e
1
b
e
a
f
u
n
ctio
n
o
f
m
ea
n
in
tr
a
-
clu
s
ter
an
d
th
e
tar
g
et
d
is
tan
ce
o
f
th
e
C
Hs.
I
n
o
r
d
er
to
s
elec
t th
e
o
p
tim
al
C
Hs,
th
e
1
to
b
e
m
in
im
ized
.
L
e
t u
s
ass
u
m
e
2
b
e
th
e
f
u
n
ctio
n
wh
ic
h
is
in
v
er
s
e
o
f
to
tal
cu
r
r
en
t
e
n
er
g
y
o
f
all
th
e
s
elec
ted
C
Hs.
I
n
o
r
d
er
t
o
p
r
o
v
id
e
b
etter
r
esu
lts
bo
th
th
e
o
b
jectiv
e
f
u
n
ctio
n
is
to
b
e
m
in
im
ize
d
an
d
it to
b
e
wi
th
in
(
1
,
2
)
∈
[
0
,
1
]
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
1
is
r
ep
r
esen
ted
as
;
min
1
=
∑
1
=
1
(
∑
(
,
)
+
(
,
)
=
1
)
(
1
2
)
wh
er
e,
(
,
)
r
ep
r
esen
ted
as
th
e
d
is
tan
ce
b
etwe
en
th
e
tar
g
et
n
o
d
e
to
th
e
clu
s
ter
h
ea
d
.
(
,
)
d
en
o
ted
as
th
e
d
is
tan
ce
b
etwe
en
th
e
clu
s
ter
h
ea
d
to
th
e
b
ase
s
tatio
n
.
an
d
d
en
o
ted
as
th
e
n
u
m
b
er
o
f
tar
g
et
s
en
s
o
r
n
o
d
es a
n
d
clu
s
ter
h
ea
d
s
.
T
h
e
o
b
jectiv
e
f
u
n
ctio
n
2
is
m
ath
em
atica
lly
r
ep
r
esen
ted
as
;
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
18
,
No
.
6
,
Dec
em
b
e
r
2
0
2
0
:
2
8
2
2
-
2
8
3
3
2828
min
2
=
1
∑
=
1
(
1
3
)
wh
er
e,
d
en
o
ted
as
th
e
r
esid
u
al
en
er
g
y
o
f
th
e
clu
s
ter
h
ea
d
.
I
n
o
r
d
e
r
to
m
in
im
ize
b
o
t
h
t
h
e
o
b
jectiv
e
f
u
n
ctio
n
,
we
u
s
e
GW
O
alg
o
r
i
th
m
to
s
elec
t
th
e
o
p
tim
al
C
H
to
lin
ea
r
ly
d
ec
r
ea
s
e
th
e
f
u
n
ctio
n
.
T
h
e
c
o
m
b
in
e
d
o
b
jectiv
e
f
u
n
ctio
n
is
m
ath
em
a
tically
r
ep
r
esen
ted
in
(
1
4
)
.
=
×
1
+
(
1
−
)
2
,
0
<
<
1
(
1
4
)
wh
er
e
is
th
e
weig
h
t
p
ar
am
et
er
in
th
e
r
an
g
e
o
f
[
0
,
1
]
.
T
h
e
s
ea
r
ch
a
g
en
t
with
m
in
im
al
o
b
jectiv
e
v
alu
e
is
co
n
s
id
er
ed
as th
e
C
H.
4
.
2
.
Clus
t
er
f
o
r
m
a
t
i
o
n
I
n
W
SN,
s
elec
tin
g
th
e
o
p
tim
al
C
Hs
will
lead
to
a
p
r
o
p
e
r
clu
s
ter
f
o
r
m
atio
n
an
d
it
aid
s
to
p
r
o
l
o
n
g
th
e
n
etwo
r
k
life
tim
e.
I
n
th
is
wo
r
k
,
we
s
elec
t
th
e
C
Hs
u
s
in
g
th
e
r
esid
u
al
en
er
g
y
,
n
eig
h
b
o
r
h
o
o
d
r
atio
an
d
d
is
tan
ce
f
r
o
m
B
S.
T
o
cr
ea
te
an
o
p
tim
al
clu
s
ter
f
o
r
m
atio
n
,
we
f
o
r
m
u
la
te
weig
h
t
f
u
n
ctio
n
wh
ich
g
u
id
es
th
e
s
en
s
o
r
n
o
d
e
to
jo
in
in
th
eir
r
esp
ec
tiv
e
C
Hs.
T
h
e
d
er
i
v
ed
weig
h
t
f
u
n
ctio
n
i
s
m
ath
em
atic
ally
r
ep
r
esen
ted
i
n
th
e
(
1
5
)
.
(
,
)
=
∗
(
)
(
,
)
×
(
,
)
×
(
)
(
1
5
)
wh
er
e
is
th
e
co
n
s
tan
t
p
ar
am
et
er
v
alu
e
(
i.e
.
=
1
)
.
(
)
r
ep
r
esen
ted
a
s
th
e
r
esid
u
al
en
er
g
y
o
f
th
e
ℎ
clu
s
ter
h
ea
d
.
(
,
)
d
en
o
ted
as
th
e
d
is
tan
ce
b
etwe
en
th
e
ith
tar
g
e
t
s
en
s
o
r
n
o
d
e
(
i.e
.
n
o
r
m
al
s
en
s
o
r
n
o
d
e
)
an
d
jth
cl
u
s
ter
h
ea
d
.
(
,
)
r
ep
r
ese
n
ted
as
th
e
d
is
tan
ce
b
etwe
en
ℎ
clu
s
ter
h
ea
d
an
d
th
e
b
ase
s
ta
t
io
n
.
(
)
d
en
o
ted
as
th
e
n
eig
h
b
o
r
h
o
o
d
r
atio
o
f
th
e
ℎ
C
H.
T
h
e
ℎ
s
en
s
o
r
n
o
d
e
with
h
ig
h
weig
h
t
v
al
u
e
ca
n
ab
le
to
jo
in
in
a
ℎ
clu
s
ter
h
ea
d
.
4
.
3
.
G
WO
a
lg
o
rit
h
m
f
o
r
CH
s
elec
t
io
n
I
n
th
e
p
r
o
p
o
s
ed
GW
O
alg
o
r
ith
m
,
th
e
s
ea
r
ch
a
g
en
t
r
e
p
r
esen
te
d
as
m
d
im
en
s
io
n
al
clu
s
ter
h
ea
d
s
with
its
p
o
s
itio
n
(
x
-
ax
is
,
y
-
a
x
is
)
an
d
s
en
s
o
r
id
as
s
h
o
w
n
in
Fig
u
r
e
3
.
I
n
itially
,
th
e
al
g
o
r
ith
m
s
elec
ts
th
e
r
an
d
o
m
clu
s
ter
h
ea
d
with
th
eir
ap
p
r
o
p
r
iate
lo
c
atio
n
s
an
d
it
co
m
p
u
tes
th
e
o
b
je
ctiv
e
v
alu
e
f
o
r
th
o
s
e
clu
s
ter
h
e
ad
s
.
Nex
t,
it
s
elec
t
s
th
e
f
ir
s
t
b
est
s
ea
r
ch
ag
e
n
t
,
s
ec
o
n
d
b
est
s
ea
r
ch
ag
en
t
an
d
t
h
ir
d
b
est
s
ea
r
ch
a
g
en
t
an
d
r
e
s
t
o
f
th
e
s
ea
r
ch
ag
en
t
as
.
W
ith
th
e
aid
o
f
th
r
e
e
b
est
s
o
lu
tio
n
s
,
th
e
r
em
ai
n
in
g
s
ea
r
ch
ag
e
n
ts
u
p
d
ate
its
p
o
s
itio
n
an
d
th
e
n
ew
p
o
s
itio
n
r
ep
r
esen
ted
as
th
e
n
e
w
clu
s
ter
h
ea
d
s
wh
ich
s
atis
f
i
es
th
e
o
b
jectiv
e
f
u
n
ctio
n
.
L
ater
,
id
en
tify
t
h
e
weig
h
t
f
u
n
ctio
n
t
o
d
eter
m
i
n
e
th
e
a
p
p
r
o
p
r
iate
clu
s
ter
m
em
b
er
s
to
j
o
in
in
th
eir
r
esp
ec
tiv
e
C
Hs.
T
h
e
wo
r
k
in
g
f
lo
w
o
f
th
e
p
r
o
p
o
s
ed
GW
O
is
p
r
esen
ted
in
Alg
o
r
ith
m
2
.
Fig
u
r
e
3
.
R
ep
r
esen
tatio
n
o
f
s
e
ar
ch
ag
en
t
in
GW
O
Alg
o
r
ith
m
2
: G
W
O
alg
o
r
ith
m
f
o
r
C
H
s
elec
tio
n
Input:
Number of sensors
=
{
1
,
2
,
…
,
}
, Population size =
Step 1:
Randomly initialize the search agent
∀
,
,
1
≤
≤
,
1
≤
≤
(
0
)
=
(
(
0
)
,
(
0
)
)
Step 2:
Calculate the fitness
(
)
Step 3:
Select
=
m
i
n
(
)
,
=
m
i
n
(
−
1
)
,
=
m
i
n
(
−
2
)
/*
-
first best solution,
second best search agent,
–
third best search agent */
Step 4:
while
(
<
)
/*
–
the maximum number of iterations */
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
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p
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t E
l Co
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2829
for
=
1
:
Update the position of search agent
Calculate the fitness
(
)
Update
,
and
end for
for
=
1
:
calculate
(
(
+
1
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(
+
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|
m
i
n
(
(
(
+
1
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,
)
)
,
∀
,
1
≤
≤
end
for
end while
Step 5:
Repeat
Step 4
until it reaches the maximum number of iterations
Output:
Visualize the best cluster heads
=
{
1
,
2
,
…
,
}
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7
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e
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.
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.
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f
o
r
m
a
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na
ly
s
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h
e
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f
o
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m
a
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ce
o
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th
e
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r
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o
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ith
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h
as
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m
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ely
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n
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,
n
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(
NL
)
an
d
p
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k
et
r
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b
y
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S
(
PR
-
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S).
T
h
ese
th
r
ee
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m
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ce
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ics ar
e
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o
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s
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alg
o
r
ith
m
with
o
th
er
alg
o
r
ith
m
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
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m
m
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n
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p
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t E
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tr
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,
Vo
l.
18
,
No
.
6
,
Dec
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b
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r
2
0
2
0
:
2
8
2
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2830
5
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1
.
P
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ir
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tly
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ted
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h
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o
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ith
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s
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y
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g
th
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m
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0
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e
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h
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m
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ce
m
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r
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f
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PS
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H
ar
e
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wn
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le
s
3
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4
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d
Fig
u
r
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s
4
-
8
in
ter
m
s
o
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t
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tal
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er
g
y
u
tili
za
tio
n
in
all
th
e
d
if
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e
n
t c
ases
.
I
n
th
e
f
ir
s
t c
a
s
e,
th
e
B
S lo
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tio
n
was
co
n
s
id
er
ed
as
m
id
o
f
th
e
n
etwo
r
k
r
eg
io
n
(
1
5
0
,
1
5
0
)
.
T
h
e
o
b
s
er
v
ed
r
esu
lts
n
o
tify
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at
th
e
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ed
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o
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ith
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ter
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ely
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n
ad
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iced
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at
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th
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m
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ich
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